theorem
 for f being Morphism of c,d holds
  c is_a_coproduct_wrt i1,i2 & dom f = c & cod f = d & f is invertible
  implies d is_a_coproduct_wrt f(*)i1,f(*)i2
proof let f be Morphism of c,d;
  assume that
A1: c is_a_coproduct_wrt i1,i2 and
A2: dom f = c & cod f = d & f is invertible;
  c is_a_coproduct_wrt (0,{0})-->(i1,i2) by A1,Th79;
  then d is_a_coproduct_wrt f*((0,{0})-->(i1,i2)) by A2,Th74;
  then d is_a_coproduct_wrt (0,{0})-->(f(*)i1,f(*)i2) by Th15;
  hence thesis by Th79;
end;
